Question

If \(P(A) = \frac{4}{15}\),then \(P(\overline{A})=\)

• A. \(\frac{13}{15}\)
• B. \(\frac{11}{15}\)
• C. \(\frac{19}{15}\)
• D. \(\frac{14}{15}\)

Answer 1

The Correct Option is B

To solve the problem, we need to find the probability of the complement of event \( A \), denoted as \( P(\overline{A}) \), given that \( P(A) = \frac{4}{15} \).

1. Understanding the Complement Rule:
In probability, the sum of the probabilities of an event and its complement is always 1. That is:

\( P(A) + P(\overline{A}) = 1 \)

2. Substituting the Given Value:
Given \( P(A) = \frac{4}{15} \), we substitute into the equation:

\( \frac{4}{15} + P(\overline{A}) = 1 \)

3. Solving for \( P(\overline{A}) \):
\( P(\overline{A}) = 1 - \frac{4}{15} = \frac{15}{15} - \frac{4}{15} = \frac{11}{15} \)

Final Answer:
The value of \( P(\overline{A}) \) is \({\frac{11}{15}} \).